Name: signal flow graph branch rules
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 16 s
Channel: JoVE

在信号流图代数中，一个节点所表示的变量值等于进入该节点的所有信号的总和。该值随后通过离开该节点的所有支路进行传递。
同方向的并联分支可用单一分支替代，该分支的增益等于原始各分支增益之和。
类似地，多个单向分支的级联连接可用一个单一分支替代，该分支的增益等于原始各分支增益的乘积。
信号流图（SFG）中的反馈系统遵循特定的代数方程，可用于推导闭环传递函数。
控制系统框图可以转换为信号流图（SFG）格式。该过程包括识别变量，将每个变量与一个节点相关联，用支路连接各节点，并在每条支路上标注相应的增益。
最后，信号流图（SFG）也可以根据一组代数方程构建。该过程涉及逐步构造，为每个变量创建节点，并根据方程将这些节点相互连接。

sfg 代数

在信号流图 (SFG) 代数中，节点所代表的值由进入该节点的所有信号的总和决定。然后，该总和值会通过离开该节点的每个分支进行传输，这使得 SFG 成为可视化和分析控制系统的强大工具。

SFG 中的每个节点都对应一个变量，节点之间的相互作用由具有相关增益的分支表示。当多个分支通向一个节点时，该节点的值是所有传入分支信号的总和。然后，传出分支将该值乘以各自的增益，传输到后续节点。

将信号引导至同一方向的并行分支可以合并为单个分支。这个新分支的增益是原始并行分支增益的总和。例如，如果两个增益为 G_1 和 G_2 的分支是并行的，则可以将它们替换为增益为 G=G_1+G_2 的单个分支。

级联分支或串联分支也可以类似地简化。所得分支的增益是原始分支增益的乘积。例如，如果两个增益为 G_1 和 G_2 的分支级联，则可以用增益为 G=G_1×G_2 的单个分支替换它们。

在反馈系统中，特定的代数方程用于推导闭环传递函数。这涉及识别反馈回路并应用适当的公式来确定系统的行为。要将控制系统的框图转换为 SFG，请按照以下步骤操作:
<ol style=" padding-left: 35px; margin: 0;">
 <li>识别变量:系统中的每个变量都与一个节点相关联。</li>
 <li>互连节点:在节点之间绘制分支来表示变量之间的关系，确保准确描绘信号流的方向。</li>
 <li>标记分支:给每个分支分配适当的增益，反映系统相应部分的传递函数。</li>
</ol>

SFG 也可以从一组代数方程中导出。此过程涉及以下步骤:
<ol style=" padding-left: 35px; margin: 0;">
 <li>识别并创建方程中每个变量的节点。</li>
 <li>根据方程定义的关系，使用分支来表示这些关系连接节点。</li>
 <li>根据方程中的系数为各分支分配增益。</li>
</ol>

通过利用这些原理，SFG 提供了一种多功能且直观的方法来分析复杂的控制系统，有助于推导传递函数并增强我们对系统动力学的理解。

SFG 代数

在信号流图代数中，一个节点所表示的变量值等于进入该节点的所有信号之和。该值随后……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Diagrams and Signal Flow Graphs

图表与信号流图

KEY TERMS AND CONCEPTS

关键术语与概念

SFG Algebra

signal flow graph branch rules

Signal flow graph (SFG) branch rules show how signals move through a control system. Each node in an SFG stands for a variable. The value at a node is the sum of all signals entering it. That summed value then travels through every branch leaving the node.

Branches connect the nodes and show the relationship between variables. Each branch has a gain, which tells how strongly the signal is passed along. When several branches enter the same node, their signals are added together. When one node sends its value to the next nodes, each outgoing branch carries that value multiplied by its own gain.

Parallel branches point in the same direction and can be combined into one branch. The gain of the new branch is the sum of the original gains, such as G1 + G2. Cascaded branches are connected in series and can also be simplified. In that case, the gain of the new branch is the product of the original gains, such as G1 × G2.

SFG algebra is also used in feedback systems to find the closed-loop transfer function. This requires identifying the feedback loop and applying the correct formula for the system. A block diagram can be converted into an SFG by identifying the variables, drawing the branches between them, and labeling each branch with the right gain. An SFG can also be built directly from algebraic equations by creating nodes for each variable, linking them by the equation relationships, and assigning branch gains from the coefficients.

Signal Flow Graph Branch Rules

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Mason's rule helps students find transfer functions from signal-flow graphs in control systems and signal processing. It gives a clear path for solving graphs that can look complicated at first. The method uses loop gains, forward-path gains, and non-touching loops to organize the calculation. A loop gain comes from tracing a path from a node back to the same node. The gain is the product of the branch gains along that loop. Each loop gain matters because it feeds into the later...

signal flow graphs

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Signal-flow graphs are a clear way to represent control systems. They offer an alternative to traditional block diagrams. In these graphs, branches stand for systems and nodes stand for signals. Arrows show the direction of signal flow, and the transfer function is written next to each arrow. Signal-flow graphs also handle subtraction in a different way from block diagrams. In a block diagram, summing junctions often use negative signs. In a signal-flow graph, those negative signs are built...

sfg algebra

Signal flow graph (SFG) branch rules show how signals move through a control system. Each node in an SFG stands for a variable. The value at a node is the sum of all signals entering it. That summed value then travels through every branch leaving the node. Branches connect the nodes and show the relationship between variables. Each branch has a gain, which tells how strongly the signal is passed along. When several branches enter the same node, their signals are added together. When one node...

key terms and concepts

Learn how signal flow graphs use nodes, branch gains, parallel and cascaded simplification, and feedback formulas to analyze control systems.

Signal Flow Graph Branch Rules | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Signal Flow Graph Branch Rules

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